When navigating the maze, the robot will only need to go north, south, east, and west. it can be useful to use the complex plane to represent these directions. when using the complex plane this way, we use numbers such that their magnitude is equal to 1. if we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west? n=i s = -i e =1 w = -1 the arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. when programming the robot, let the complex number d represent the direction the robot is facing. as the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. at the start of the maze, what is the value of d? d=1 while navigating the maze, the robot will need to be able to turn left and right. the first turn the robot will make is a left turn. what will the value of d be after the first turn?
East = 1
South = - i
West = -1
We are given that, the robot can only go north, south, east and west.
Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.
Now, it is provided that the ' i ' represent that robot is facing north.
So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.
Since, the values on y-axis are negative in that direction.
Hence, South will be represented by ' - i ' .
Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.
So, the value that represents East will be 1 ( as it is on the positive x-axis ).
Since, west is in the opposite direction of east.
So, West will be represented by -1.
S = -i
W = -1
If facing north is represented by i, then facing south would be the opposite or -i.
We can let facing east be 1 because the magnitude has to be 1, so facing west would be the opposite or -1